THEORY OF THE PERFECT GAME © 2008 John Vrooman - Vanderbilt University USA

COMPETITIVE BALANCE IN Monopoly SPORTS LEAGUES © 2008 John Vrooman - Vanderbilt University USA

John Vrooman Vanderbilt University, USA © 2008 John Vrooman - Vanderbilt University USA

$M/w 2 $M/w 1 LEAGUE EQUILIBRIUM A cT MR 2 cT MR 1 w1w1 © 2008 John Vrooman - Vanderbilt University USA

$M/w 2 $M/w 1 REVENUE SHARING IN PROFIT LEAGUE A cT MR 2 cT MR 1 B MR 1 ′ MR 2 ′ w1w1 © 2008 John Vrooman - Vanderbilt University USA

CT’ $M/w 2 $M/w 1 OPEN & CLOSED PROFIT LEAGUES A cT A’ CT’ MR 1 w1w1 MRP 2 MR 1 MRP 1 MR 2 © 2008 John Vrooman - Vanderbilt University USA

CT ’ $M/w 2 $M/w 1 INVARIANCE PROPOSITION A cT A’ CT ’ MR 1 w1w1 MRP 2 MR 1 MRP 1 MR 2 MR 1 ′ MR 2 ′ MRP 1 ’ MRP 2 ’ B © 2008 John Vrooman - Vanderbilt University USA

$M/w 2 $M/w 1 PAYROLL CAP IN PROFIT LEAGUE A cT MR 2 cT MR 1 w1w1 CAP 1 C’T B © 2008 John Vrooman - Vanderbilt University USA

$M/w 2 $M/w 1 REVENUE SHARING & Payroll cap A cT MR 2 cT MR 1 C’ MR 1 ′ MR 2 ′ w1w1 CAP 1 B C C’T © 2008 John Vrooman - Vanderbilt University USA

$M/w 2 $M/w 1 REVENUE SHARING & Payroll MINIMUM A cT MR 2 cT MR 1 MR 1 ′ w1w1 CAP 1 B C MIN 2 C’T C’’T B’ MR 2 ′ © 2008 John Vrooman - Vanderbilt University USA

$M/w 2 $M/w 1 REVENUE SHARING & Payroll MINIMUM A cT MR 2 cT MR 1 MR 1 ′ w1w1 MIN 1 B MIN 2 C’T C’’T B’ MR 2 ′ © 2008 John Vrooman - Vanderbilt University USA

AR 1 MR 2 A cT AR 2 MR 1 $M/w 2 $M/w 1 SPORTSMAN WIN-MAX LEAGUE B cT © 2008 John Vrooman - Vanderbilt University USA

AR 1 AR 2 ’ A cT AR 1 ’ $M/w 2 $M/w 1 SPORTSMAN REVENUE SHARING B cT AR 2 © 2008 John Vrooman - Vanderbilt University USA

AR 1 A C’T AR 2 $M/w 2 $M/w 1 SPORTSMAN PAYROLL CAP C’T CAP 2 CAP 1 B  c’T © 2008 John Vrooman - Vanderbilt University USA

AR 1 AR 2 ’ A cT AR 2 AR 1 ’ $M/w 2 $M/w 1 REVENUE SHARING & PAYROLL CAP B cT CAP 2 CAP 1 C’T C © 2008 John Vrooman - Vanderbilt University USA

w t = w t -1 w t = a + b w t-1 + e t w t =.500 Win t Win t -1 b = 0 b = 1 a a = 0 a =.500 Beta Balance © 2008 John Vrooman - Vanderbilt University USA

National Football League © 2008 John Vrooman - Vanderbilt University USA

Major League Baseball © 2008 John Vrooman - Vanderbilt University USA

National Basketball Association © 2008 John Vrooman - Vanderbilt University USA

National Hockey League © 2008 John Vrooman - Vanderbilt University USA

English Premier League © 2008 John Vrooman - Vanderbilt University USA

French Ligue 1 © 2008 John Vrooman - Vanderbilt University USA

German Bundesliga © 2008 John Vrooman - Vanderbilt University USA

Italian Serie A © 2008 John Vrooman - Vanderbilt University USA

La Liga Española © 2008 John Vrooman - Vanderbilt University USA

Finis © 2008 John Vrooman - Vanderbilt University USA